A308057 Lexicographically earliest sequence of positive terms such that for any distinct m and n, a(m) + 2*a(m+1) <> a(n) + 2*a(n+1).

1, 1, 2, 1, 3, 3, 4, 1, 6, 1, 7, 5, 7, 7, 8, 1, 12, 1, 13, 8, 2, 7, 12, 3, 15, 10, 5, 16, 3, 18, 3, 19, 12, 7, 19, 14, 7, 21, 15, 19, 18, 6, 13, 22, 6, 15, 22, 8, 16, 13, 24, 10, 18, 15, 24, 13, 26, 13, 27, 21, 25, 24, 15, 30, 13, 32, 13, 33, 24, 18, 22, 21

Offset

1,3

Comments

The sequence becomes linear after some chaotic initial terms.

Links

Rémy Sigrist, Table of n, a(n) for n = 1..2000

Formula

a[n+72] = a[n] + 24 for any n > 847.

Example

The first terms, alongside a(n) + 2*a(n+1), are:
  n   a(n)  a(n)+2*a(n+1)
  --  ----  -------------
   1     1              3
   2     1              5
   3     2              4
   4     1              7
   5     3              9
   6     3             11
   7     4              6
   8     1             13
   9     6              8
  10     1             15

Prog

(PARI) s=0; v=1; for(n=1, 72, print1(v", "); for (w=1, oo, if (!bittest(s, x=v+2*w), s+=2^x; v=w; break)))

Crossrefs

See A308058 for the multiplicative variant.

See A308059 and A308073 for other variants.

Sequence in context: A304037 A265144 A263275 * A097686 A082666 A363619

Adjacent sequences: A308054 A308055 A308056 * A308058 A308059 A308060

Keyword

nonn

Author

Rémy Sigrist, May 10 2019

Status

approved